• Pierre De La Harpe

      Articles written in Proceedings – Mathematical Sciences

    • Constructing irreducible representations of discrete groups

      Marc Burger Pierre De La Harpe

      More Details Abstract Fulltext PDF

      The decomposition of unitary representations of a discrete group obtained by induction from a subgroup involves commensurators. In particular Mackey has shown that quasi-regular representations are irreducible if and only if the corresponding subgroups are self-commensurizing. The purpose of this work is to describe general constructions of pairs of groups Γ0 with Γ its own commensurator in Γ. These constructions are then applied to groups of isometries of hyperbolic spaces and to lattices in algebraic groups.

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